Selected by NASA in April 1996, Brown reported to the Johnson Space Center in August 1996. He completed two years of training and evaluation, and was qualified for flight assignment as a mission specialist. He was initially assigned to support payload development for the International Space Station, followed by the astronaut support team responsible for orbiter cockpit setup, crew strap-in, and landing recovery.

Brown flew aboard Space Shuttle Columbia on STS-107, logging 15 days, 22 hours, and 20 minutes in space from January 16 to February 1, 2003. The flight was a dedicated science and research mission. Working 24 hours a day, in two alternating shifts, the crew successfully conducted approximately 80 experiments. The mission ended abruptly on February 1, 2003, when Columbia's crew perished during entry, 16 minutes before the scheduled landing.